Chaos Forgets and Remembers: Measuring Information Creation, Destruction, and Storage

Ryan G. James; Korana Burke; James P. Crutchfield

doi:10.1016/j.physleta.2014.05.014

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arXiv · 1309.5504

Chaos Forgets and Remembers: Measuring Information Creation, Destruction, and Storage

Ryan G. James·Korana Burke·James P. Crutchfield

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Abstract

The hallmark of deterministic chaos is that it creates information---the rate being given by the Kolmogorov-Sinai metric entropy. Since its introduction half a century ago, the metric entropy has been used as a unitary quantity to measure a system's intrinsic unpredictability. Here, we show that it naturally decomposes into two structurally meaningful components: A portion of the created information---the ephemeral information---is forgotten and a portion---the bound information---is remembered. The bound information is a new kind of intrinsic computation that differs fundamentally from information creation: it measures the rate of active information storage. We show that it can be directly and accurately calculated via symbolic dynamics, revealing a hitherto unknown richness in how dynamical systems compute.

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Ryan G. James, Korana Burke, James P. Crutchfield. 2013-12-17. Chaos Forgets and Remembers: Measuring Information Creation, Destruction, and Storage. https://doi.org/10.1016/j.physleta.2014.05.014

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